Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model

In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtaining improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the setting and convergence analysis of the data assimilation algorithm

Self-Avoiding Walk on the square site-diluted Ising-correlated lattice

The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean field relation is tested to measure the effect of correlation. After exploring a perturbative Fokker-Planck-like equation, we apply an enriched Rosenbluth Monte Carlo method to study the problem. To be more precise, the winding angel analysis is also performed from which the diffusivity parameter of Schramm-Loewner evolution (SLE) theory ($\kappa$) is extracted. We find that at the critical Ising (host) system the exponents are in agreement with the Flory's approximation. For the off-critical Ising system we find also a new behavior for the fractal dimension of the walker trace in terms of the correlation length of the Ising system $\xi(T)$, i.e. $D_F^{\text{SAW}}(T)-D_F^{\text{SAW}}(T_c)\sim \frac{1}{\sqrt{\xi(T)}}$

Reply to “Comments on “Consensus and Cooperation in Networked Multi-Agent Systems””

[No abstract

On Steering Swarms

The main contribution of this paper is a novel method allowing an external observer/controller to steer and guide swarms of identical and indistinguishable agents, in spite of the agents' lack of information on absolute location and orientation. Importantly, this is done via simple global broadcast signals, based on the observed average swarm location, with no need to send control signals to any specific agent in the swarm

Perturbative Analysis of Spectral Singularities and Their Optical Realizations

We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte

Reply to Head-Gordon and Paesani: Liquid water, a branched polymer with ∼100-fs short-lived heterogeneous hydrogen bonds

The letter by Head-Gordon and Paesani (hereafter HG-P) (1) contains several confusions about our results that we clarify here. The title claiming that liquid water is not a dynamic polydisperse branched polymer is not supported by any information in their letter

The quantum mechanics-based polarizable force field for water simulations

We report here a new force field for water based solely on quantum mechanics (QM) calculations with no empirical data. The QM was at a high level, coupled cluster single double triple, for all orientations and distances for water dimer plus X3LYP density functional theory (DFT) on 19 larger water clusters. In addition, we included charge and polarization based on the polarizable charge equilibration method and nonbond interactions from DFT-D3 calculations on the H_2 and O_2 crystal. This model, denoted as RexPoN, provides quite excellent agreement with experimental (expr) data for the solid and liquid phase of water: T_(melt) = 273.3 K (expr = 273.15 K) and properties at 298 K: ΔH_(vap) = 10.36 kcal/mol (expr = 10.52), density = 0.9965 gr/cm^3 (expr = 0.9965), entropy = 68.4 (J/mol)/K (expr = 69.9), dielectric constant = 76.1 (expr = 78.4), and ln D_s (self-diffusion coef) = −10.08 (expr = −11.24). Such an accurate force field for water will, we believe, be useful for full solvent calculations of electrocatalysis, where we can restrict QM water to just the first one or two layers involving reactions, using RexPoN to provide the polarization for a more distant solvent. Also, RexPoN may provide a better description of the solvent for proteins, DNA, polymers, and inorganic systems for applications to biomolecular, pharma, electrocatalysis (fuel cells and water splitting), and batteries where interaction with explicit water molecules plays a significant role

Effects of dietary protein and energy levels on growth and body composition of Caspian trout larva (Salmo trutta caspius)

A 3t2 factorial feeding trial of three dietary protein levels (45, 50 and 55%) and two dietary crude energy levels (4200 and 4600 cal/g) with three replications was conducted to investigate the proper dietary protein and energy levels for the growth of fingerling Caspian trout (Salmo trutta caspius). Fingerlings with average weight of 135 plus or minus 0.24mg were fed the experimental diets for 45 days